Brian, if you still have the top part with the leaves, I would not give up on it yet. Try cutting off the rotted part, let the cut end dry, then stick it in a pot? Mist the leaves until you have roots agaon.
Plummies grow nicely in the ground here. I got one as a gift from my daughter a few years ago. She went to Hawaii for her honeymoon and brought it back for me, just a shriveled stick in a bag. I was very doubtful, but today it is a lovely 5ft. shrub and is blooming right now. (it's dark out or I'd post a picture). I did just what you did, and mine also went mushy in the middle and flopped over. I ignored it, it was depressing me so much, and darned if the top part, lying despondently on the ground, didn't put out little roots and keep growing!
I also have one that was in the garden here when we bought the house. We had two record cold winters, '09 and '10 and it died right back to the ground. Both years it came back from the roots. I have not seen hide nor hair of it since 2 years ago, but darned if it isn't putting up new leaves again this year! I'm going to pot it up and give it a new home if it will keep rising like the phoenix. It's a lovely red one.
Point is, these things are resilient! Here's a shot of my Hawaiian one from last year.